U.S. Pat. No. 6,400,100 has already disclosed an operating method, an electronic ballast and a system for resonant operation of high-pressure lamps in the longitudinal mode. This document specifies a method for finding the second longitudinal acoustic resonant frequency. This is based on the assumption that when the frequency range which contains the longitudinal mode is scanned continuously, the resonant frequency in the vertical operating position can be found by the occurrence of a relative operating voltage increase for the lamp. It is self-evident that this method results in the longitudinal frequency being found, and then maintained, for a segregated, that is to say demixed, state of the plasma located in the discharge vessel at vertical resonance. This frequency found in this way can, however, be located considerably too high depending on the filling composition of the metal halide filling and the time by which the search procedure is carried out, so that stimulation of the acoustic resonance at the frequency found using the abovementioned method results in inadequate thorough mixing, and does not sufficiently well cancel out the segregation, that is to say the demixing of the plasma. Furthermore, the implementation of the operating method in suitable components of an electronic ballast is complex.